Question: Simplify the following expression: $k = \dfrac{9x^2 - 36x + 27}{x - 3} $
Explanation: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $9$ , so we can rewrite the expression: $ k =\dfrac{9(x^2 - 4x + 3)}{x - 3} $ Then we factor the remaining polynomial: $x^2 {-4}x + {3} $ ${-3} {-1} = {-4}$ ${-3} \times {-1} = {3}$ $ (x {-3}) (x {-1}) $ This gives us a factored expression: $\dfrac{9(x {-3}) (x {-1})}{x - 3}$ We can divide the numerator and denominator by $(x + 3)$ on condition that $x \neq 3$ Therefore $k = 9(x - 1); x \neq 3$